Controlled $g$-dual frames and their approximates in Hilbert spaces

Year 2022, Volume: 51 Issue: 2, 421 - 429, 01.04.2022

Sayyed Mehrab Ramezani

https://doi.org/10.15672/hujms.784819

Abstract

In this paper, we introduced and characterized the controlled $g$-duals of a frame in a separable Hilbert space $\mathcal{H}$ . Afterwards, we obtained new $C$-controlled $g$-dual frames from the given $C$-controlled $g$-dual frames. In addition, the approximation for controlled $g$-dual frames was defined and some of their properties were investigated. Finally, we characterized the relationship between approximately $C$-controlled dual and $C$-controlled $g$-dual.

Keywords

frames, controlled frames, g-dual frame, approximate g-dual

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